Electromagnetism & electromagnetic induction：練習問題

Which of the following correctly describes the magnetic field lines inside the central region of a long current-carrying solenoid?

A square loop with sides of length \(0.1\text{ m}\) is placed in a uniform magnetic field of strength \(0.5\text{ T}\). The plane of the loop makes an angle of \(30^\circ\) with the magnetic field lines. What is the magnetic flux through the loop?

Four long parallel wires are fixed at the corners of a square \(PQRS\) (ordered clockwise). Wires at \(Q\), \(R\), and \(S\) carry currents out of the paper of equal magnitude. The wire at \(P\) carries a current of the same magnitude into the paper. What is the direction of the net magnetic field at the center of the square?

A long, straight conductor carries a steady current flowing vertically upwards. Which of the following diagrams best represents the magnetic field lines produced around the conductor?

A rectangular conducting loop is being pulled out of a uniform magnetic field of strength \(B\) at a constant velocity \(v\). The side of the loop that is perpendicular to the direction of motion has a length \(L\). What is the magnitude of the induced e.m.f. across the loop as it leaves the field?

Using Lenz's Law, explain the direction of the induced current in a closed conducting loop when the north pole of a bar magnet is moved towards it.

An ideal step-down transformer has a primary coil with \(1000\) turns and a secondary coil with \(50\) turns. If the primary voltage is \(220\text{ V}\) and the secondary is connected to a \(10\text{ }\Omega\) resistor, calculate the primary current.

An ideal step-up transformer with a turn ratio \(N_p : N_s = 1 : 40\) is used to transmit \(40 \text{ kW}\) of power from a \(250 \text{ V}\) source. If the transmission lines have a total resistance of \(15 \Omega\), calculate the power loss in the lines and the overall efficiency of the power transmission system.

A long solenoid is connected to a d.c. power supply. A student wants to investigate the magnetic field produced by the solenoid.

(a) Describe the pattern of the magnetic field lines inside and outside the solenoid when a current flows through it. (1 point)

(b) The student places a small compass near one end of the solenoid. If the current flows in a clockwise direction when viewed from that end, state whether that end acts as a North pole or a South pole. Explain your answer using the right-hand grip rule. (2 points)

A long solenoid of length 0.40 m is wound with 800 turns of wire. A steady current of 2.5 A flows through the solenoid. An electron is injected into the center of the solenoid at a speed of \(4.0 \times 10^6 \text{ m s}^{-1}\) in a direction perpendicular to the axis of the solenoid.

(a) Calculate the magnetic flux density \(B\) at the center of the solenoid.
(b) Determine the magnitude of the magnetic force acting on the electron at the instant it enters the solenoid.
(c) Describe the subsequent path of the electron inside the solenoid, assuming the magnetic field is uniform. Justify your answer.

(Given: \(\mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}\), charge of electron \(e = 1.6 \times 10^{-19} \text{ C}\))